Professional Investor

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1 Autumn Professional Investor Autumn 2013 Diversification, Correlation, and Asset Allocation Volume 23 number 3 ISSN Professional Investor I m not advocating returning to where we were but I do want to stop and think about where capital is going and whether our banks compete on an international level. Jessica Ground, ASIP Diversification, correlation, and asset allocation Globalisation versus home country bias Capturing the illiquidity premium in your portfolio Listed real estate as a diversifier Behavioural biases The Official Journal of the CFA Society of the UK supporting asip, cfa & imc professionals A risk-factor approach to asset allocation

2 Professional Investor Feature Behavioural biases and not-so-optimal portfolio construction Too much reliance on mathematical modelling is outright misleading and supports behavioural biases that lead to fragility, say Kerrin Rosenberg and Theo Kocken. The dynamics of the real world are often very different from, sometimes even opposite to, the models we conveniently embrace. Portfolio construction is seen by many in the industry as a quantitative exercise leading to an efficient frontier portfolio. Although over the decades it has been adjusted in many directions, it still rests on the foundations of Markowitz and Sharpe. The basic assumption is that a known probability distribution with known parameters can be used to deliver an optimal risk adjusted return. For institutional investors with future liabilities that are possible to estimate, this risk return is often chosen against a liability benchmark, representing the future retirement cashflows. One popular variant these days is the risk-parity concept, based on the idea that each asset class or type of investment should contribute an equal amount of risk to the portfolio. Similar to the early stage simple Markowitz model, Executive summary Well researched behavioural biases are at the root of our inclination to rely too much on mathematical models in finance. This leads to fragile portfolio construction and regular unexpected once-in-a-lifetime surprises that threaten the long-term objectives of institutional investors. Portfolio construction needs to rely less on often misleading measures such as volatility and more on common sense measures that limit the lethal negative consequences of unexpected events, including convexity seeking strategies that create protection against adverse market events. risk-parity still relies on very specific mathematical models and assumptions that are usually derived from recent history. Under the efficient frontier school, portfolio construction requires assumptions about expected return and risk for each asset, as well as the relationships between the various assets. Risk is usually replaced by volatility (standard deviation of returns), and correlations are used to describe a general relationship between assets. Optimisation techniques are then used to derive so called efficient portfolios which provide the highest expected return for a given level of risk, or alternatively, that provide the lowest levels of risk for a given expected return. Uncertainty, not probabilities Now all this makes perfect sense if the price of assets in financial markets follows stochastic processes with normal distributions. Or, using a much less strict assumption, if prices follow a known distribution, maybe a bit less smooth than the Gaussian model, for example with stochastic volatility etc. But the problem is that we don t know the exact distribution of financial variables. We have to deal with uncertainty in the financial world, not with probabilities. Risk does not equal volatility and correlation is a very poor simplification for describing the rich and complex interactions between assets. Frank Knight, in his famous 1921 book Risk, Uncertainty and Profit, claims that a measurable risk is in effect no true uncertainty at all. The uncertainty we are faced with doesn t follow known distributions. In Antifragility (2012), Nassim Taleb explains that we indeed do not know the distributions we are faced with in financial markets. And if we concede we don t know the distributions exactly, then we should steer in a very different way to lead to more robust solutions. In fact, if we steer according to rules based on very specific model assumptions (that we know are merely convenient, and surely not correct), we move our portfolios into fragility. Actually this is what we do most of the time, and every time we fail, we come up with more complex modelling based on even more specific assumptions. Paradoxically, not accepting that we simply do not know (or know much less than we think we know) gets us caught by surprise every time another shock hits the markets. The Journal of the CFA Society of the UK 29

3 Feature Professional Investor One of the reasons that we can t know the statistical distribution of financial variables is because market shocks are often endogenously driven ie made by men. The reactions of 6 billion people participating in financial markets are very unpredictable. The result is that we have to face regular meltdowns which are wrongly perceived as Black Swans anomalies that can stand outside the model s predictions because they are claimed to be so rare. Yet financial crises and other so called tail-risk events occur frequently and with remarkably similar characteristics. The enormous build up of household debt, usually connected to a property bubble, is, for example, a theme that runs through many financial crises. The same for high price/earnings ratios, often explained as a new era instead of an unsustainable anomaly. Cognitive and behavioural biases So if the existing models are so deficient, why, as an industry, are we so obsessed with them? Over the last few decades, we have learned a lot from cognitive sciences. With special thanks to pioneers like Daniel Kahneman, Amos Tversky and Paul Slovic, much was revealed about how we persistently make inconsistent choices and have cognitive biases that may explain our tendency to make mistakes in modelling and decision making. One of the behavioural flaws people face stems from the concept of ambiguity aversion. Already examined in the 1960s, psychologist Daniel Ellsberg found that people prefer to work in a world with known probabilities rather than in a world with uncertainty where a probability distribution is not available. As an example, most people would rather play a game where they know the probabilities than a game which lacks probabilities, even if this is not to their advantage. This is probably one of the reasons we have a strong tendency to work with probability models such as Gaussian models, even when we know from experience that the financial markets exhibit very different characteristics than Gaussian shocks. There is another bias that supports our use of probability models, even if they can be falsified quite easily. When we have a belief in (read: a desire for) a mathematically smooth world, and are confronted with information that both supports and rejects this vision, we have a strong inclination to accept the information that confirms our prior beliefs and reject or degrade the research that challenges our beliefs. In 1979 Charles Lord conducted research that revealed that when two groups of people have opposite ideas and both groups get access to exactly the same information with evidence both for and against their ideas the differences in opinion don t converge but polarise even more. Since our Cartesian, Western society has a strong belief in applying mathematics and statistics to science, not only to hard sciences like physics, but even to a social science like finance, we use our confirmation filter to confirm our belief the world can be modelled with numerical precision. We ignore Hayek s wisdom: physics is unorganised complexity, economics is organised complexity. The dynamics of financial markets change with the behaviour of people and numerical predictions are unjustified, constituting only a pretence of knowledge. According to the 2002 Nobel Prize winner, Daniel Kahneman, one of the most dangerous failures of intelligent men is overconfidence. Experiments reveal that people attach a much higher probability that they are correct in their predictions and estimates than they actually are. To make things worse, overconfidence increases with the amount of information we receive, even if this information contains no relevant content for the problem at hand. This is very detrimental, bearing in mind we live in a world with an overload of information that is irrelevant but perceived as containing lots of explanatory features. 30 The Journal of the CFA Society of the UK

4 Professional Investor Feature Figure 1: S&P Stock index versus VIX (implied) volatility index S&P /07/ /07/ /07/ /07/2009 Source: Bloomberg The problems of working with data Another problem in the art of portfolio construction is working with data. We rely on data when using our models. What else can we do? Now the problem with data is that they can be very misleading. For example, when markets do very well for a while, often the perception of risk decreases. This is partially due to overconfidence but is also supported by the affect heuristic, as researched by Paul Slovic: when people have a good feeling about the returns of the markets, their perception of the risks in the markets is lower. This is exactly what we saw during many crises in the past: the more risk accumulated (exploding stock and house prices etc), the lower the volatility in the markets. Using volatility as an indicator for risk is extremely tricky in periods that are most relevant for proper risk management and long term returns. Figure 1 emphasises this phenomenon. The S&P 500 index doubled in four years at the same time the volatility index an indication of the market s perception of risk decreased by more than 60%. We are not arguing that all models are useless in understanding financial behaviour. But too much reliance on mathematical modelling is not just spurious, it s outright misleading and it supports and even reinforces several of the behavioural biases described above that lead to fragility. This is all the more true when it comes to mean variance optimisation, where the outcomes are particularly sensitive to many spurious inputs and assumptions. So portfolio construction relying too much on mathematical modelling is tricky, as the dynamics of the real world are often VIX very different, sometimes even opposite, from the models we conveniently embrace. A better approach to portfolio construction What would a better portfolio construction model look like? One that isn t overly reliant on backwards-looking quantitative models. There are several key principles we suggest. Be the tortoise rather than the hare. A portfolio that aims for more consistent, modest performance (while risking small losses) is preferable to a hero/zero approach. The reason is simple you can t ever be that confident about any one risk paying off, so it s better to assume that a high proportion of your investment views won t pay off as expected and therefore take a large number of smaller risks so that you can more easily recover from losses that will inevitably occur. Diversifying in this way only helps, however, if the range of investments respond in different ways to different economic outcomes, which leads to the next principle. Robustness to multiple scenarios. Scenario analysis isn t new, but in many investment processes it is an afterthought a challenge that can easily be forgotten in the face of chasing returns. Scenario analysis needs to be embedded into the heart of portfolio construction we need to constantly be thinking about scenarios we hope are unlikely, their impact on markets and how the portfolio will be affected. Obvious scenarios include severe recession, financial crisis and high inflation (stagflation). Scenario analysis should be the lens through which the portfolio is judged. We need to make sure that the portfolio is not overly exposed to any one economic outcome. This involves controlling the degree of exposure such that losses will be limited and bearable if an adverse scenario develops. Described this way, scenario analysis is a forward-looking process that relies on a fundamental understanding of the drivers of return and risk in each investment. Historic analysis of performance behaviour of say the last few years or even decades may be of little value in forming a sensible understanding of an asset s likely behaviour in the future. There is no easy formula and no substitute for going back to economic fundamentals. A scenario approach will involve making some quantitative assessment of what to expect from each asset class under different scenarios. And scenarios need to be designed based on, among others, deleverage and debt-deflation running out of control or serious inflationary stagnation as a result of unprecedented money The Journal of the CFA Society of the UK 31

5 Feature Professional Investor printing programmes. But the range of outcomes will certainly be far wider than is implied by Gaussian distributions. Be willing to pay for protection. An asset that provides protection in adverse scenarios (eg put options, inflation-linked fixed income etc), might, in isolation, be expected to lose money. However, this doesn t mean that the investment doesn t have a useful role to play in the portfolio. We need to consider the overall impact at a portfolio level. For example, protective assets (like put options) reduce the anticipated outcome in a benign scenario, but they provide a much better outcome in adverse scenarios like recessions and financial crises. For resilience-seeking investors, this is a very sensible trade-off. That is, forgoing some upside when things are good so that you suffer less and even profit from market circumstances during the hard times. Seek convexity in the portfolio. Many investments provide linear payoffs they have equal capacity to surprise on the up and down sides. However, other investments are non-linear. Their outcomes are skewed one way or the other, and they may become more or less sensitive as underlying markets move. A classic example is a call option that has limited downside, and a sensitivity to markets that increases as markets rise. Some asset classes also exhibit natural convexity such as certain assetbacked securities. Further, convexity can be created through a trading style (e.g. applying stop losses). Introducing convexity to the portfolio can strengthen the crash-resistance of the portfolio without giving in too much on return. Demand a very high reward from illiquidity. Investors are repeatedly duped into illiquid investments that offer only marginally higher returns than similar, liquid ones. Liquid investments have the huge advantage that you can change your portfolio when the facts change. In summary Several cognitive biases make us inclined to be overly reliant on mathematical models that don t fit reality. Actually, in the circumstances in which you need them the most, like in the run up to a crisis, key variables, such as volatility, are misleading as risk indicators. Robust investment management, based on a more humble approach regarding our limited knowledge, builds on a scenario approach that does not rely on probabilities or riskpredictors. Quantitative assessments and assumptions have a role to play, but rather than assuming the mathematical distribution of outcomes is known, the goal is to simply avoid unacceptable consequences and create convexity. This all serves the goal of good and more sustainable results for the stakeholders. Profiles Theo Kocken Theo Kocken is founder and CEO of the Cardano Group, a specialist in risk orientated investment management and risk management strategies. He holds a bachelor s degree in business administration and a Master s degree Profile in econometrics. He gained his PhD at the VU University (Amsterdam), where he is a professor of risk management. Between 1990 and 2000 he was the head of the market risk departments at ING and Rabobank International, before founding Cardano in He is the author and co-author of numerous books and articles in the area of risk management and pension funds. Kerrin Rosenberg Kerrin Rosenberg is CEO of Cardano in the UK. He graduated from the University of Manchester with a BA in economics, specialising in econometrics. He is also a fellow of the Institute of Actuaries. From 1992 to 2007 he worked as an investment consultant with Hewitt Associates in London. He is a former partner of Bacon & Woodrow, before its merger with Hewitt. In 2007 he left Hewitt to set up the Cardano Group s UK business. He has advised over a dozen of the UK s largest corporate pension funds with combined assets of over 50 billion. 32 The Journal of the CFA Society of the UK